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Math HL P3 Series & Diff. Equations


sim_pod

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Unorthodox... Agreed! What did you think of the difficulty, though? I thought the last two questions were just ridiculous! And the differential equation too! What the hell happen to all the tests for convergence that I spent so much time studying for? Ahh... IB is just not fair! :(

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The first three questions were okay, the last two were hardcore. Agreed.

The integral in 3. wasn't this difficult, all it took was to notice that v^2+2v+2=v^2+2v+1+1=(v+1)^2+1 which happened to fit in the standard integral for arctan.

I'm very glad there was an Euler question, 8 points for 1 minute of work... You just input the equations in the calculator and write down what it spits out.

The integral in the fourth question was funny, everybody in my class had to cheat with the negative signs in order to get the right result ;)

Also, the last point in the last question was two points for nothing, because all the equations from previous points were there in the questions, so you just had to substitute n=1000 into them to get the two points. Each point matters, you know...

And I must say I hated the Maclaurin bracket multiplication in the first question - I repeated it twice but I'm quite sure I still got it wrong.

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The first three questions were okay, the last two were hardcore. Agreed.

The integral in 3. wasn't this difficult, all it took was to notice that v^2+2v+2=v^2+2v+1+1=(v+1)^2+1 which happened to fit in the standard integral for arctan.

I'm very glad there was an Euler question, 8 points for 1 minute of work... You just input the equations in the calculator and write down what it spits out.

The integral in the fourth question was funny, everybody in my class had to cheat with the negative signs in order to get the right result ;)

Also, the last point in the last question was two points for nothing, because all the equations from previous points were there in the questions, so you just had to substitute n=1000 into them to get the two points. Each point matters, you know...

And I must say I hated the Maclaurin bracket multiplication in the first question - I repeated it twice but I'm quite sure I still got it wrong.

Hahaha! Yes, yes I had to cheat with the negative signs too! ;) I figured out that the next part, or the one where you had to prove the integral, it was a geometric series! I didn't have time to do it though.

Honestly, the integral in 3 just messed with my head, and I eventually gave up. I knew it was possible to factorize the RHS before actually rearranging the equation, but I was so not bothered!

I also made silly mistakes in the Maclurin series, so I had to repeat it too!

But.. Overall, not a fair paper! Hoping for a 6 maximum!

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For MajorMajor:

I also first tried to do Maclaurin series multiplication, but then I found it was easier to just calculate the derivates and substitute in 0 for each of them... Oh well..

And the thing with noticing it, yeah, try to notice it under time pressure and with that adrenaline level coursing through your veins... Still noticed though :P

But yeah, the last 2 questions were really unexpected, not like anything from past papers... Managed to do N°4 with the geometric series and integral (and without cheating and sign manipulation) since I'm quite a math junkie... Oh yah, I really like this option...

The last question was nasty.. It wasn't, like, hard hard, it just took an awfull amount of time I didn't have in the end.. Did some parts of it though..

But yah, overall the exam was kind of harder than previous ones because of the last two questions.. But to be honest, I am more relaxed right now about the options paper than about P1 or P2.. All the mistakes I did there, my mind just screams "How could you have not known?! You have been doing this sooo often before.." Argh..

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By far the most difficult paper I have ever seen. The last one I did was November 2010... no comparison... I managed to do 4a) and b) but 5? what the hell? since when are you supposed to find series if you are given a sum? i just hope the grade boundaries are very low. all the other options seem to have been quite doable. I was very grateful for the 6 odd points one could get cheaply in 5. if everything i ahve done is right, ill get 40/60 - IF.

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Guest Red XII

I'm hoping the grade boundaries will be easy. While the first three questions were fairly typical, the fourth question was extremely unorthodox and the fifth was just plain difficult.

Usually there's a lot more L'Hopital and infinite series convergence/divergence, which I was counting on, because I'm good at those topics and DiffEQ but a bit hesitant on Taylor/Maclaurin series.

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I managed to scrape most of the points from question 5, to be honest.

In part a, |x| belongs to R, which is expected, as a factorial n! is of more dominant magnitude than any x^n.

In the second part I justified the inequality by seeing that the right was actually an alternating series (which approximated the other sidew), so if we took even terms of the series it had to be an underestimation (3 terms - overestimation,4 terms - underestimation etc.).

Number 4 I ran out of time when attempting to do finish c).

Diff. Equation didn't realize it was just (u+1)^2+1 in the denominator, *sigh*...

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Before the exam day, I reviewed all paper 3s from 08 to 10. But this paper still threw me off, question 4 is just atrocious. Din't even attempt to use b to solve c. Question 5 actually isn't that difficult, which I managed to make through. The trick lies in the substitution of x with 1/n. That differential equation I just went with my instinct and managed to use arctan.

Overall, an difficult but not entirely unmanageable paper.

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Yeah I agree. The paper was pretty unorthodox and failry difficult. No one in my class got the arctan thing in section 3. I fortunately got it at the very last minute.

So, do you guys think IB will keep low boundaries for our option this year because the other options seem to have been very easy. I am seriously hoping for low boundaries to compensate for this and paper 1.

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